QUANTITATIVE ESTIMATES OF THE ERROR IN MAINTAINING THE FORMATION OF UNDERWATER VEHICLES WITH DELAYS IN NAVIGATION DATA
Abstract
The influence of delays in receiving navigation information on maintaining a formation of underwater vehicles in the leader-followers mode is studied. The study is based on the assumption of a gradient principle of formation control during movement. The complexity of the problem is due to the unknown trajectory of the leader, incomplete knowledge and non-stationarity of the environment, and measurement errors. The obtained results are independent of the configuration of vehicles in the formation. It is shown that it is sufficient to study the influence of navigation delays on the motion of a single vehicle. Key assumptions: the trajectory of the leader is unknown; all interactions between the leader and follower vehicles are synchronized; the leader transmits its coordinates to the other vehicles at a certain frequency; displacements of the follower from its position in the formation can occur in any spatial direction. It is assumed that between receiving data on the leader's position, the follower vehicle moves in a straight line in a direction that can be chosen in many ways. One option for choosing such a direction is considered, and a mathematical model of the motion is constructed. Since the moment of information receipt is unknown, a nonlinear law is used to describe the follower's motion, taking into account the distance to the target point. Estimates of the vehicle's deviation from the target position in the formation at each moment in time are found, as well as average estimates of its deviation over the time interval between receiving navigation information and over the entire trajectory. An upper bound for the integral deviation is proposed and substantiated, allowing for a simple interpretation of the factors influencing deviation and formation breakdown.
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